Possible to bake boolean difference or use "exact" only when "fast" fails?
You can add both booleans, but disable the exact boolean. Then, you can keyframe their toggles on frame 0, by hovering over the buttons and pressing I. Then, you can go to the first frame, where you need exact boolean, toggle between the booleans, and again use I to keyframe them. Then on the first frame after that, where you no longer need exact, you can again toggle them and keyframe them, and so on.